A faucet is used to add water to a large bottle that already contained some water. after it has been filling for 4 seconds, the gauge on the bottle indicates that it contains 12 ounces of water. after it has been filling for 11 seconds, the gauge indicates the bottle contains 26 ounces of water. let y be the amount of water in the bottle x seconds after the faucet was turned on. write a linear equation that relates the amount of water in the bottle, y, to the time x.

The problem gives us points (4, 12) and (11,26). We first find the slope using m=(y2-y1)/(x2-x1). We substitute and get m=(26-12)/(11-4). This simplifies to m = 2. We can then use the point-slope form y-y1 = m(x-x1). We substitute and get y - 12 = 2(x - 4). We distribute: y - 12 = 2x - 8. We add 12 to both sides to get our final answer, y = 2x + 4.

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ap8997154 ap8997154 · Answer 2 · 2022-06-11T12:58:48+02:00

The linear equation that relates the amount of water in the bottle, y, to the time x is y=2x+4.

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c.

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

Given the water in the bottle after 4 seconds was 12 ounces, while the water in the bottle after 11 seconds is 26 ounces. Therefore, the rate of water filling in the bottle will be,

Rate = (26 - 12)ounces/(11 - 4)seconds = 14ounces/7 seconds = 2 ounces/second

Therefore, we can write the linear equation as,

y = 2x + c

Now to get the value of C, substitute the value of x as 4 while the value of y as 12. Therefore,

12 ounces = 2(4 seconds) + C

12 = 2(4) + c

12-8 = c

c = 4

Hence, the linear equation that relates the amount of water in the bottle, y, to the time x is y=2x+4.

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